Case study for the IGS ultra-rapid orbit requirements

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Case study for the IGS ultra-rapid orbit
requirements

• Jan Douša
• Miami Beach, June 2-6, 2008

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Outline

• quality of IGS ultra-rapid orbit prediction
• effect of ephemeris errors on ZTD (PPP case)
• effect in network solution
• simulation in network analysis
• summary

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Monitoring the quality of IGU orbits

• IGU w.r.t IGR orbits
• comparison in terrestrial system after Helmert
  transformation
• 3 Helmert rotations estimated epoch by epoch
  (15min) for relevant satellites only
• fitted portion compared in 0-24 hours
• predicted portion compared on hourly basis
  (1,2,3,4,.., 23)
• monthly orbit prediction statistics evaluated
• accuracy code validated with IGU x IGR orbit
  differences
• the orbit quality and the accuracy codes
  validated separately

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2004-2008 time-series of IGU orbit predictions
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Eclipsing periods
plots generated from the IGS ACCs IGUxIGR
comparison summary tables
two times per year every satellite undergoes
eclipsing period (in yellow)
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Orbit quality dependance on the prediction
orbit accuracy with respect to the prediction
interval (monthly statistics)
GPS Block IIR-M
GPS Block IIA
GPS Block IIA
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Accuracy code validation (6h prediction)
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Effect of ephemeris errors on PPP ZTD

• Basic GPS carrier phase observable (scaled to
  distance)
• Lrecsat ?recsat c.?sat c.?rec ?.nrecsat
  ?ION ?TRP ?recsat
• ?recsat .. receiver-satellite distance in vacuum
• ?TRP .. troposphere path delay we
  approximate as 1/cos(z) ZTD
• The ephemeris error is projected into the
  observables via a unit vector directing from
  receiver to satellite
• Rrecsat / Rrecsat ?Xsat e recsat ?Xsat
• e recsat Rz (?sat) Rz
  (?sat) . ?XRACsat
• We are interested in Radial/Along-track/Cross-trac
  k component errors, but we distinct only Radial
  and Tangential (Along-track Cross-track)
  components and we do not need to consider the
  satellite track direction.
• Generalizing the situation to be independent of
  the receiver/satellite positions, we express the
  errors as zenith dependent only
• e recsat . Rz (?sat) Rz (?sat) . ?XRAC sat
  cos(?) ?XRadsat sin(?) ?XTansat
• where ? arcsin(sin(z) . Rrec/Rsat)
• is a paralax for the satellite between the
  geocenter and the station.
• Putting equal the projected orbit errors with
  troposphere model we get an impact

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Orbit errors in PPP ZTD
Point positioning

• Radial error
• impact1.0 in zenith
• impact0.0 in horizon
• Tangential error
• depends on track orientation
• max impact0.13 (45deg)
• min impact0.00 (0-90deg)

• Assumption
• orbit errors only ZTD
• (usually also in ambiguities, clocks)

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Effect in network solution

• In network double-difference observables are
  used
• Lklij Lkli Lklj ( Lki Lli ) ( Lkj
  L lj )
• but for single satellite error we can consider
  only single difference for baseline, relevant
  portion of the observation equation is
• Lkli R ki-R li (e ki e li ) ?X i
  cos(zki) ZTD k - cos(zli) ZTD l ...
• Again, we distinguish the Radial and Tangential
  error only and we project them into the
  receiver-satellite distance as zenith (or
  paralax, ?) dependant function
• (e ki e li ) Rz (?i) Rz (?i) . ?XRACi (
  cos(?ki) ?XRadi sin(?ki) ?XTani )
• 
  ( cos(? li) ?XRadi sin(? li) ?XTani )
• but we need the coordinates for estimating the
  zenith angle at the second station.
• Studying the two marginal cases we can keep a
  general description limited only by defining the
  baseline lenght 1000 km
• equal azimuths satellite and second station are
  in equal azimuths
• equal zeniths zeniths to satellite are equal
  for both stations
• We calculate the impact in ZTD if the error is
  not absorbed by other parameters.

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Radial orbit error in DD ZTD
Network solution

• Radial error
• impact0.0 cancelled in case of equal zeniths
• max impact ?0.0023 (38deg) in case of equal
  azimuths
• min impact-gt0.0 above the baseline or close
  to horizon

Assumption (1000km) orbit errors only
ZTD (usually also by ambiguities)
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Tangential orbit error in DD ZTD
Network solution

• Tangential error
• depends on satellite track orientation with
  respect to baseline
• max impact ?0.027 is above the mid of baseline
  for both cases and orbit error paralalel to
  baseline
• impact reduced always when error is
  perpendicular to baseline
• impact reduced with decreasing elevation
  (slightly different for both cases)

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Simulation in network analysis

• Network
• - 16 sites approx. 1000km distances
• - star baselines strategy from central point
• Solution
• - synthetic (constant) errors (1,5,10,25,100cm)
  introduced in the orbits consequently in radial,
  along-track and cross-track component for
  selected satellite
• - pre-processing of 24h data with the original
  IGS final orbits
• - ZTD estimated with original IGS final orbits
  (reference ZTD)
• - ZTD estimated with biased orbits (tested ZTD)
• - ZTD estimated with ambiguities free (estimated
  simultaneously)
• - ZTD estimated with ambiguities fixed (using
  original IGS orbits)
• comparison of resulted ZTDs

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Effects of the synthetic orbit errors in ZTD
Synthetic error in orbit position 1m in
along-track (G01, G03, G05)
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Effect of the synthetic orbit errors in ZTD (2)
Ambiguity fixed
Ambiguity free
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Orbit requirements particular example

• Note solving for the ambiguities significantly
  helps to overcome the limits in quality of the
  predicted orbits (and predicted accuracy codes)
• network solution
• baselines 1000 km (ZTD bias reduces to
  half if 500km)
• max 1cm error in ?ZTD
• requirements 217cm in radial and 19cm in
  tangential direction
• PPP solution
• max 1cm error in ZTD
• requirements 1cm in radial and 7cm in tangential
  direction
• currently IGU prediction quality observed
• prediction length 1-9h for NRT/RT
• nominal situation 1cm 3-5cm
  2-3cm RAO rms
• during eclipsing period 1-3cm 4-20cm
  3-8cm RAO rms

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Summary requirements for ZTD

• network solution (ZTD) is negligibly sensitive to
  the radial error, but along (cross)-track errors
  can occasionally affects the ZTDs. The baseline
  configuration plays a crucial role during such
  period - only specific baselines are sensitive in
  specific situation and unfortunatelly the
  averaging with respect to other satellite
  observables is limited.
• PPP solution (ZTD) depends on the accuracy of
  radial component (100 in zenith) in nominal
  situation, but on the along(cross)-track
  component for eclipsing Block-IIA satellites.
  Fortunatelly, error averaging performs over all
  the satellites. Satellite clocks (especially in
  regional solution) can absorb significant portion
  of the radial error.
• the ambiguities are in both cases able to absorb
  a significant portion of the orbit errors and
  currently help to reduce the effect.
• only a few weakly predicted satellites occur in a
  single product, thus usually a robust satellite
  checking (and excluding) strategy applied by the
  user should be satisfactory in many cases for the
  network solution, although as much as satellites
  is generally requested.

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Summary quality of IGU prediction

• after decommission of satellite G29 (October,
  2008) there is no more significant difference in
  the standard orbit prediction performance.
• different pattern of the prediction can be seen
  during the eclipsing periods. We have to
  distinguish between satellites of old Block-IIA
  (fastly degrading) and new Block-IIR (modestly
  degrading) types.
• there are still 14 15 of old-type satellites
  active (45) G01, G03, G04, G05, G06, G08, G09,
  G10, G24, G25, G26, G27, G30, G32.
• accuracy codes are in most cases relevant for the
  prediction, but usually underestimated for
  Block-IIA during eclipsing periods and at the
  start of the maintenance periods.
• currently 1-9h prediction are at least necessary
  for NRT/RT usage
• shorter prediction will be appreciated especially
  due to old Block-IIA satellites, but mainly for
  the NRT/RT (global) PPP applications.
• Relevant question to ACs how simply they can
  provide the orbits upgraded every 3h (2h delay
  ?) with the same quality as of today ?
• (Even higher update rate could be requested for
  the PPP solutions).